Inframarginal Choice Plus Time: Path Dependence

Traditional marginal analysis relies on continuously-divisible decisions that imply finely tuned marginal adjustments as external parameters change. As a result, the problem of being locked-in to a decision rarely arises.^[23] A lock-in or path-dependent process, in simplest terms, is one in which it is costly or impossible to alter one's current path of decisions.

An entrepreneur cannot merely command an indian restaurant into existence but must instead take many and varied steps to sequentially “assemble” such a restaurant. As mentioned above, she must decide on where to locate, which equipment to purchase, what items to list on the menu, and so on. Each of these subsidiary decisions generally involves three stages. The first is a search or decision-making process wherein the entrepreneur gathers information and decides upon specific inputs. Second, some production input is purchased or contracted for. Third, once the input is obtained, she must integrate it into her production process.

For example, before a Tandoori oven can be purchased for this Indian restaurant, our entrepreneur must travel to an equipment supplier or, at the very least, visit a website and decide which of multiple ovens she should purchase.

We break out the multiple stages of acquiring an oven because standard marginal analysis tends to assume away these other, niggling stages and their associated costs, which most will recognize as transaction costs.^[25] Normally, economists ignore these costs for one of two reasons: either it is presumed the costs of these other stages are not sufficiently important to register them independently, or it is assumed the decision-maker has taken account of them before purchasing the input of interest; the latter implies the transaction costs can be simply wrapped into the traditional cost functions.

Contrary to the standard treatment, we do not believe the transac­tion costs of deciding upon, acquiring, and integrating capital assets into the production process are trivial for entrepreneurial processes; more­over, simply adding them to the standard cost of the input is analytically misleading because their costs cannot be recouped like that of the asset itself, as we hope to show.^[26]

To begin, we want to emphasize that these costs are borne across each decision the entrepreneur must make. Cumulatively, transaction costs can be a significant factor in production, particularly for entrepreneurs who are combining or recombining assets. Indeed, we can think of the cost of the entire process of combining assets in some new way, or for some new venture, as transaction costs, since they are costs that are incurred in the actual process of combining inputs and not part of the input itself; they cannot be recouped like the value of the asset can potentially be.^[27] We argue these transaction costs create a wedge between the value of the current path of decisions, in which prior transaction costs have been sunk, and alternative paths of decisions, in which transaction costs have yet to be experienced.

When the entrepreneur wishes to buy a capital good, she must suffer transaction costs in addition to the purchase price. These transaction costs plus the purchase price constitute the full outlay to acquire the good. Notice that even if there were no transaction costs for reselling—nor any deterioration in the quality of the capital good, defined as depreciation— she would not be able to recoup the transaction costs outlaid to acquire the asset in the first place.

There are, of course, also transaction costs in reselling a capital good. Were the entrepreneur to resell her capital goods, she must figure out where to sell them, how much to sell them for, and she will have to deal with the potential buyers who are interested in purchasing the capital good. potential buyers may want to test or inspect the capital good for quality, requiring the entrepreneur to spend time showcasing it. There may then be transaction costs in the form of “bargaining costs” over the price and exchange conditions. Finally, the new owner will have to take possession, potentially inflicting yet further transaction costs should the assets require special services or equipment to move. Taken together, the entrepreneur simply cannot liquidate her capital goods in the ways often assumed in standard microeconomics: transaction costs form a wedge between the status quo and either acquiring or dispensing of assets.

This argument may be clearer with a very simple one-period example of the choice to become an entrepreneur. in choosing between her current occupation and starting a business, our potential entrepreneur is expected to consider her possible paths before beginning down a new one. one path is her current job where she earns a salary, s. In previous periods, she suffered the transaction costs of finding and acquiring that job, but those transaction costs are sunk, and we ignore them. Her alternative path involves a very simple business startup that requires only one capital good or asset, A, to function successfully.

Traditional analysis suggests that, as long as our entrepreneur expects π0 > s, she will prefer to become an entrepreneur over staying on her current job path. Critical to our analysis, however, expected returns must be higher than her salary by at least tb to induce her to leave her current job. This is how tb acts as a wedge between her expected profit from the business and her current earnings.

Now, we add a second period after our decision-maker has begun down her entrepreneurial path. She would have already outlaid resources, t_b, to pay for the transaction costs of acquiring the asset. If she continues to make payments on the asset, her new profit equation will be πι = R-a—v. Even if she owns the asset outright and her balance sheet reflects that ownership, she cannot resell it at zero cost. To do so requires the kinds of transaction costs we suggested above, such as marketing and any other costs of liquidating it. The aggregate costs of each of the steps can be designated as the transaction costs of sale, or t_s. In other words, she only recoups the value of the asset less the transaction costs of the sale. Thus, the opportunity costs of remaining on her current entrepreneurial path (s - t_s) is less than they were before becoming an entrepreneur (s).³2 It is also true that π₀ = R-a-t_b-v < πι = R-a-v, and π₁∕(s - t_s) > π₀∕s, meaning the expected relative returns to entrepreneurship have increased once she starts down her entrepreneurial path.

³¹Of course, each term is an expectation, so profit should be understood as expected profit; we ignore the expectation operator for simplicity.

³²To simplify the analysis, we assume that our agent's previous employer will allow her to return to her original job any time she wants. We therefore assume away any transaction costs to finding a new job if her entrepreneurial path does not work out. Relaxing this highly unrealistic assumption creates an even greater wedge than the one we describe here.

Reconsider the decision problem in the initial period. The then- potential entrepreneur wondered what it would cost her to start the business, which was the forgone salary plus the transaction costs of acquiring the necessary asset. By contrast, if the entrepreneur considers returning to her salaried position after the second period, she must sell the asset. Both comparisons entail transaction costs, and therefore trans­action costs encourage the individual to stay on her current path because transaction costs create a wedge that raise the relative cost of the alterna­tive path. In broader terms, transaction costs on both the acquisition and disposal side of assets associated with starting a business create a wedge between any given existing path and her imagined paths.

Our model is intentionally simple, as it comprises only one capital good and we assume away any potential transaction costs of making deci­sions over variable inputs. However, as we repeatedly mentioned above, following an entrepreneurial path requires hundreds or thousands of deci­sions on the path toward forming a business: entrepreneurship is a choice between bundles of decisions. consider how the model changes with hundreds of capital goods and transaction costs associated with securing variable inputs. scores of transaction costs will be incurred to launch the venture and thus the entrepreneur’s expectation of benefits (pecuniary and nonpecuniary) from the enterprise will have to be greater than the sum of these transaction costs in order to choose the entrepreneurial path.

in anticipating the expected net benefits from staying in her current employment versus opening a restaurant, our potential entrepreneur should consider the possibility the venture will not succeed or that she might want to exit someday. If so, we would expect her to consider all the potential transaction costs before commencing. In other words, before moving to the entrepreneurial path, her initial profit expectation must be π'₀ = R-a-tt>-t_s —v, which is similar to πo, except for the addi­tional cost of t_s. Forward-looking entrepreneurs must acquire numerous capital goods and know that any potential exit from the startup will entail transaction costs of both buying and selling those assets, increasing the potential wedge between current salary and expected profits.^[28]

A simple inequality illustrates that forward-looking entrepreneurs will likely face greater “lock-in” to whatever path they are currently on. A traditional cost-benefit comparison of whether to leave one's salaried job to start a business would ask the following question: are revenues minus costs greater than the alternative employment, or is R — C ≥ s (where C ? a + v)? In other words, the would-be entrepreneur is expected to leave her current salaried job when she expects profit to exceed her salary. However, with a little algebra, our equation π'₀, above, suggests the forward-looking potential entrepreneur would need R — C ≥ s + [t⅛ + t_s], meaning the wedge, or “hurdle” to leave one's current career path is higher—by the amount of both the purchasing and selling trans­action costs—than the simple “profit versus salary” comparison suggests. This higher hurdle will tend to lock-in would-be entrepreneurs to their current career paths: we should expect fewer people to overcome these hurdles—to become entrepreneurs—than in simpler models that ignore the transaction costs associated with these kinds of decisions.

As time passes, a second key facet of entrepreneurship leads to path dependence: learning. Over time, agents learn, which means that once our entrepreneur sets up and runs her restaurant, she is likely to get better at it. In short, over time she becomes more productive at that particular function. Her improved entrepreneurial skills mean she will be able to produce more for a given hour of work effort than when she first started.^[29]

Entrepreneurial learning is, however, unlikely to lead to improvements in skills not related to her current entrepreneurial position. Even if the

knowledge and skills from her previous salaried position do not deterio­rate, she will be relatively more productive at her current position because her productivity as an entrepreneur will increase while her productivity at her old job will, at best, remain idle. Indeed, we can think of the time our restaurateur spends on her entrepreneurial path, itself, as an asset (or her time is effectively transformed into an asset through learning) that she cannot easily sell.^[30] Learning to set up and run an Indian restau­rant is unlikely to have considerable value outside of running restaurants. The entrepreneur’s skills at running an Indian restaurant cannot be sold or transferred to someone else without incurring additional transaction costs.^[31] Thus, if she exits her current business, she loses the productivity growth that resulted from her time spent as an entrepreneur. As such, an additional wedge between continuing with the present path or switching paths can be attributable to learning.^[32]

Consider, furthermore, how much more the relative net benefits of staying on her current path would increase (versus moving back to her previous job) if her formerly-used skills deteriorate during the time that she is an entrepreneur. If her previous skills do deteriorate—and we expect they generally do—then the increased productivity from time spent learning in the new entrepreneurial path presents an even greater wedge compared with her declining productivity in her previous employ­ment. We would expect it will be even more difficult for her to get a job—even at her old position—at a similar salary level, the more time she spends as an entrepreneur. This theoretical point would seem to be supported amply by the stylized fact that those who spend time outside their profession receive lower wages than those who do not.

Because of these two wedges—one arising from the transaction costs of acquiring assets or assembling assets into a “firm,” and the other arising from the entrepreneur’s increased productivity in her new profes­sion relative to her declining productivity in her previous profession—she is likely to be locked-in, at least to some degree, to her current path. In fact, consider the simple calculations to decide whether our entrepreneur should exit her venture, an exercise similar to the one above when she decided whether to leave her job to start a business. In this case, the simple, non-transaction cost model inequality would be: R — C ≤ s, implying profits would have to fall below her salary in paid employment. Transaction costs, however, complicate the inequality: with transaction costs, profitability will be compared with her potential salary minus the transaction costs of selling the assets, or R — C ≤ s — t_s. Thus, the entrepreneur is likely to stay in the business longer than most models without transaction costs would predict.^[33] If we add in the deterioration in productivity in the old career—i.e., her returning salary, s' < s—the inequality is further exacerbated, and the individual is likely to remain with her business under even more unfavorable circumstances.

In sum, we hope we have shown that transaction costs involved in the buying and selling of assets and in “forming” the firm in the first place give rise to some degree of path dependence. Looking at a single deci­sion, as marginal analysis typically does, transaction costs may not appear substantial. However, across bundled entrepreneurial choices, transac­tion costs might well be substantial and therefore substantially affect the relative opportunity costs of decisions confronting the entrepreneur or potential-entrepreneur. These transaction costs cannot, moreover, be simply added to the asset cost itself, but the asset can, presumably, be resold less the transaction costs of resale. Additionally, entrepreneurs learn—which means they become more productive—and this increased productivity creates an additional wedge making path dependence more likely. The entrepreneur or would-be entrepreneur will find it more diffi­cult to switch life and career paths than is suggested in more traditional models. This is another way of describing the discontinuous nature of decisions surrounding entrepreneurship.

While path dependence is likely under the conditions we specify, we want to be clear that we are not suggesting that path dependence is synonymous with inefficiency, as much of that literature presumes. On this matter, Demsetz’s (1969,1) foundational critique on the notion that “the relevant choice.[is] between an ideal norm and an existing ‘imperfect’ institutional arrangement” still applies. He goes on to suggest,

This nirvana approach differs considerably from a comparative institu­tion approach in which the relevant choice is between alternative real institutional arrangements. In practice, those who adopt the nirvana view­point seek to discover discrepancies between the ideal and the real and if discrepancies are found, they deduce that the real is inefficient. Users of the comparative institution approach attempt to assess which alternative real institutional arrangement seems best able to cope with the economic problem. (1969, 1, emphasis in original)

In other words, it seems a pointless exercise to compare the real imper­fect choices confronting entrepreneurs with some set of idealized choices that are unattainable. Furthermore, there is nothing in our approach that suggests any other entity has access to any better information or decision­making framework. Thus, while our entrepreneurs might be “locked in” to a given path that they themselves wish they could escape more easily, that option is no more real than wishing away the other difficult constraints they face, such as disappointingly low prices for their product.